It depends on how developer made the application.
By default compiled app will support "Any CPU", but if developer choose only RT it won't start on x86. But I doubt developers will choose only ARM version.

Why do people think that RT apps don't work on the Smart? Of course they do!

What Ray says is perfectly correct (I have an app in the store myself), and I chose to publish ARM, x86 and x64 versions because it's a no-brainer and doesn't require any extra work. I'd expect close to 100% of developers to be doing the same.